Alex Y
You're making better progress than I did on this one.

I think you can say that for each student that represents a prime number, those lockers will be closed at the end, since they will be the only students to reach those lockers.

Don't confuse locker numbers with student numbers. A better way to say this is that locker number p, where p is prime, will have its state changed only by students 1 and p, thus ending in the closed state.